Hydrophobic hydration processes: General thermodynamic model by thermal equivalent dilution determinations

The “hydrophobic hydration processes” can be satisfactorily interpreted on the basis of a common molecular model for water, consisting of two types of clusters, namely WI and WII accompanied by free molecules WIII. The principle of thermal equivalent dilution (TED) is the potent tool (Ergodic Hypothesis) employed to monitor the water equilibrium and to determine the number ξw of water molecules WIII involved in each process. The hydrophobic hydration processes can be subdivided into two Classes: Class A includes those processes for which the transformation A(−ξwWI → ξwWII + ξwWIII + cavity) takes place with the formation of a cavity, by expulsion of ξw water molecules WIII whereas Class B includes those processes for which the opposite transformation B(−ξwWII − ξwWIII → ξwWI − cavity) takes place with reduction of the cavity, by condensation of ξw water molecules WIII. The number ξw depends on the size of the reactants and measures the extent of the change in volume of the cavity. Disaggregating the thermodynamic functions ΔHapp and ΔSapp as the functions of T (or lnT) and ξw has enabled the separation of the thermodynamic functions into work and thermal components. The work functions ΔGWork, ΔHWork and ΔSWork only refer specifically to the hydrophobic effects of cavity formation or cavity reduction, respectively. The constant self-consistent unitary (ξw = 1) work functions obtained from both large and small molecules indicate that the same unitary reaction is taking place, independent from the reactant size. The thermal functions ΔHTh and ΔSTh refer exclusively to the passage of state of water WIII.Essential mathematical algorithms are presented in the appendices.